Question

In case of flat belt open drive, if the centre distance between pulleys is 2 m and both pulleys are equal in diameter of 1 m; then the length of the belt in meters is:

• A. $(2 + \pi)$
• B. $(4 + \pi)$
• C. $(6 + \pi)$
• D. $(8 + \pi)$

Hint:

For equal pulleys, the belt touches exactly half of each pulley ($2 \times 1/2 \text{ circumference} = \pi D$) and travels the center distance twice ($2x$). [cite: 15, 37]

Answer 1

The Correct Option is B

1. General Formula for Open Belt Drive: [cite: 23, 25] The length $L$ is given by: $$L = \pi(r_1 + r_2) + 2x + \frac{(r_1 - r_2)^2}{x}$$ Where $r_1, r_2$ are radii and $x$ is the center distance. [cite: 23, 25]

2. Simplification for Equal Pulleys: [cite: 23, 25] Since both pulleys have a diameter of 1 m, their radii are $r_1 = r_2 = 0.5$ m. [cite: 23, 25] When $r_1 = r_2$, the term $\frac{(r_1 - r_2)^2}{x}$ becomes zero. [cite: 23, 25] The formula simplifies to: $$L = \pi(D) + 2x$$ [cite: 23, 25]

3. Calculation: [cite: 23, 25] Given $D = 1$ m and $x = 2$ m: $$L = \pi(1) + 2(2)$$ [cite: 23, 25] $$L = \pi + 4$$ [cite: 23, 25] The length of the belt is $(4 + \pi)$ meters. [cite: 23, 25]